Function finds indices of taxonomic diversity and distinctness, which are averaged taxonomic distances among species or individuals in the community (Clarke & Warwick 1998, 2001)
taxondive(comm, dis, match.force = FALSE)
taxa2dist(x, varstep = FALSE, check = TRUE, labels)Function returns an object of class taxondive with following items:
Number of species for each site.
\(\Delta\), \(\Delta^*\), \(\Delta^+\), \(s\Delta^+\) and \(\Lambda^+\) for each site.
Standard deviation of \(\Delta^+\).
Expected values of corresponding statistics.
Function taxa2dist returns an object of class "dist", with
an attribute "steps" for the step lengths between successive levels.
Community data.
Taxonomic distances among taxa in comm. This should
be a dist object or a symmetric square matrix.
Force matching of column names in comm and
labels in dis. If FALSE, matching only happens when
dimensions differ, and in that case the species must be in identical
order in both.
Classification table with a row for each species or other basic taxon, and columns for identifiers of its classification at higher levels.
Vary step lengths between successive levels relative to proportional loss of the number of distinct classes.
If TRUE, remove all redundant levels which are
different for all rows or constant for all rows and regard each row
as a different basal taxon (species). If FALSE all
levels are retained and basal taxa (species) also must be coded as
variables (columns). You will get a warning if species are not
coded, but you can ignore this if that was your intention.
The labels attribute of taxonomic distances. Row
names will be used if this is not given. Species will be matched by
these labels in comm and dis in taxondive if
these have different dimensions.
Jari Oksanen
Clarke & Warwick (1998, 2001) suggested several alternative indices of taxonomic diversity or distinctness. Two basic indices are called taxonomic diversity (\(\Delta\)) and distinctness (\(\Delta^*\)):
| \(\Delta = (\sum \sum_{i<j} \omega_{ij} x_i x_j)/(n (n-1) / 2)\) |
| \(\Delta^* = (\sum \sum_{i<j} \omega_{ij} x_i x_j)/(\sum \sum_{i<j} x_i x_j) \) |
The equations give the index value for a single site, and summation goes over species \(i\) and \(j\). Here \(\omega\) are taxonomic distances among taxa, and \(x\) are species abundances, and \(n\) is the total abundance for a site. With presence/absence data both indices reduce to the same index \(\Delta^+\), and for this index Clarke & Warwick (1998) also have an estimate of its standard deviation. Clarke & Warwick (2001) presented two new indices: \(s\Delta^+\) is the product of species richness and \(\Delta^+\), and index of variation in taxonomic distinctness (\(\Lambda^+\)) defined as
| \(\Lambda^+ = (\sum \sum_{i<j} \omega_{ij}^2)/(n (n-1) / 2) - (\Delta^+)^2\) |
The dis argument must be species dissimilarities. These must be
similar to dissimilarities produced by dist. It is
customary to have integer steps of taxonomic hierarchies, but other
kind of dissimilarities can be used, such as those from phylogenetic
trees or genetic differences. Further, the dis need not be
taxonomic, but other species classifications can be used.
Function taxa2dist can produce a suitable dist object
from a classification table. Each species (or basic taxon) corresponds
to a row of the classification table, and columns give the
classification at different levels. With varstep = FALSE the
successive levels will be separated by equal steps, and with
varstep = TRUE the step length is relative to the proportional
decrease in the number of classes (Clarke & Warwick 1999).
With check = TRUE, the function removes classes which are distinct for all
species or which combine all species into one class, and assumes that
each row presents a distinct basic taxon. The function scales
the distances so that longest path length between
taxa is 100 (not necessarily when check = FALSE).
Function plot.taxondive plots \(\Delta^+\) against Number of
species, together with expectation and its approximate 2*sd
limits. Function summary.taxondive finds the \(z\) values and
their significances from Normal distribution for \(\Delta^+\).
Clarke, K.R & Warwick, R.M. (1998) A taxonomic distinctness index and its statistical properties. Journal of Applied Ecology 35, 523--531.
Clarke, K.R. & Warwick, R.M. (1999) The taxonomic distinctness measure of biodiversity: weighting of step lengths between hierarchical levels. Marine Ecology Progress Series 184: 21--29.
Clarke, K.R. & Warwick, R.M. (2001) A further biodiversity index applicable to species lists: variation in taxonomic distinctness. Marine Ecology Progress Series 216, 265--278.
diversity.
## Preliminary: needs better data and some support functions
data(dune)
data(dune.taxon)
# Taxonomic distances from a classification table with variable step lengths.
taxdis <- taxa2dist(dune.taxon, varstep=TRUE)
plot(hclust(taxdis), hang = -1)
# Indices
mod <- taxondive(dune, taxdis)
mod
summary(mod)
plot(mod)
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